Correlations in Finite Fermi Systems - Semiclassics and Shell Structure

Abstract: This dissertation investigates correlations in finite Fermi systems. The atomic nuclei is the mainly studied system but also other systems, like superconducting metallic grains and cold Fermionic gases are considered. The dissertation comprises of five original papers. Paper I and II investigates the autocorrelation function of the difference between experimental and theoretical nuclear masses. This quantity is found to agree with estimates of Periodic Orbit theory assuming underlying chaotic dynamics. In Paper III and IV a semiclassical theory for the BCS pairing gap is developed. It is found to agree well with experimental data for nuclei. It is also applied to other finite systems, superconducting metallic grains and cold Fermionic gases. Paper V considers an extension of the BCS theory called the Particle Number Projection method. The pairing shell energy is calculated using the Strutinsky method for a large number of nuclei across the nuclear chart. It is found that the BCS and projection methods give very similar results for the pairing shell energy.